LPV Modeling and Robust Control of closed kinematic chains using the exchange method

The Two-Input Two-Output Port (TITOP) approach enables the modular modeling of flexible multi-body systems, incorporating uncertainties and varying geometric parameters through Linear Fractional Transformations (LFT). These models can thus be directly used for robust control synthesis and analysis. However, exact LFTs cannot be derived for every closed kinematic chain since there can be non-rational constraints between the geometric parameters. In this paper, approximated LFTs of these constraints are found using optimal polynomial approximations obtained with the exchange method. This approach is applied to the robust control of a flexible four-bar mechanism.